Hosts Spain will take on last year’s runners-up Croatia in the Davis Cup quarter-finals in Malaga in November.
The Netherlands and the United States, who both beat Great Britain in Group D of qualifying, face Australia and Italy in the last eight respectively.
Germany will play Canada in the other quarter-final match.
The Davis Cup knockout stage starts on 22 November at the Martin Carpena Arena with the final taking place five days later.
Spain, champions in 2019, knew they had to beat winless South Korea to advance in the final round of group ties on Sunday.
Straight-set wins for Roberto Bautista Agut and world number one Carlos Alcaraz in the singles saw them cruise to the last eight.
Alcaraz had suffered a 6-7 (3-7) 6-4 6-2 defeat by Canada’s Felix Auger-Aliassime on Friday in what was his first match since winning the US Open.
However, the 19-year-old beat Kwon Soon-woo 6-4 7-6 (7-1) and Bautista Agut defeated Hong Seong-chan 6-1 6-3 to secure their place in the knockout stages.